A SUPERCONVERGENT <i>L</i><sup>∞</sup>-ERROR ESTIMATE OF RT1 MIXED METHODS FOR ELLIPTIC CONTROL PROBLEMS WITH AN INTEGRAL CONSTRAINT

Yuelong Tang; Yuchun Hua

doi:10.11948/2017065

2017 Volume 7 Issue 3

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Yuelong Tang, Yuchun Hua. A SUPERCONVERGENT L∞-ERROR ESTIMATE OF RT1 MIXED METHODS FOR ELLIPTIC CONTROL PROBLEMS WITH AN INTEGRAL CONSTRAINT[J]. Journal of Applied Analysis & Computation, 2017, 7(3): 1037-1050. doi: 10.11948/2017065

Citation:

Yuelong Tang, Yuchun Hua. A SUPERCONVERGENT L^∞-ERROR ESTIMATE OF RT1 MIXED METHODS FOR ELLIPTIC CONTROL PROBLEMS WITH AN INTEGRAL CONSTRAINT[J]. Journal of Applied Analysis & Computation, 2017, 7(3): 1037-1050. doi: 10.11948/2017065

A SUPERCONVERGENT L^∞-ERROR ESTIMATE OF RT1 MIXED METHODS FOR ELLIPTIC CONTROL PROBLEMS WITH AN INTEGRAL CONSTRAINT

Yuelong Tang^1,2,
Yuchun Hua¹

1 College of Science, Hunan University of Science and Engineering, 425100 Yongzhou, China;
2 School of Mathematical Sciences, Peking University, 100871 Beijing, China

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Abstract

Abstract

In this paper, we investigate the superconvergence property of mixed finite element methods for a linear elliptic control problem with an integral constraint. The state and co-state are approximated by the order k=1 Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. A superconvergent approximation of the control variable u will be constructed by a projection of the discrete adjoint state. It is proved that this approximation have convergence order h² in L^∞-norm. Finally, a numerical example is given to demonstrate the theoretical results.
- Elliptic equations /
- optimal control problems /
- superconvergence /
- mixed finite element methods /
- postprocessing
MSC: 49J20;65N30

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References

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